Question

What is the centre of a mass in a ring on it's geimatrical centre

Answer 1

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A point about which moment of point masses of a body is zero, is known as center of mass. That is if required, r1, r2…….are the distances of points of masses m1, m2, m3 …..etc

Sum of (m1r1+m2r2+m3r3+………….miri)=0

When a body is placed in a uniform gravitational field then

(m1gr1+m2gr2+m3gr3+………. . ……..+migri)=0

That is center of gravity of a body is the point about which sum of the moments of all the gravitational forces is zero. The above expression is equivalent to the above expression shown for center of mass.Thus CG of a body coincides with its CM.

The CG of a ring is the center of circle of which it is made.Moment of mass points of a ring about this point is zero.